27th All Russian Mathematical Olympiad Problems 2001

1.  Are there more positive integers under a million for which the nearest square is odd or for which it is even? 2.  A monic quartic and a monic quadratic both have real coefficients. The quartic is negative iff the quadratic is negative and the set of values for which they are negative is an interval of length more than 2. Show that at some point the quartic

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